Weston, 22, who joined the Bees from Notts County in the summer of 2009, only signed a new three-year deal at Griffin Park before Christmas.
The Owls are understood to have made an approach for the former England under-17 international with Brentford chief executive Andrew Mills confirming last week that a number of clubs have been interested in their star players but they have no intention of selling.
Weston told the Hounslow Chronicle: "I saw they (Sheff Wed) have made an approach, other than that I haven't heard anything.
"But I'm happy at Brentford. I feel I'm still improving and have still got two-and-a-half years left on my contract.
"We're only seven points off the play-offs. It's a tight league so if we can get back on a run there's no reason we can't be up there."